Wavelet transform and anti-Wick quantization of time

Abstract

Coherent states are fundamental objects in quantum physics and in mathematics. In this short note, we use coherent states as the basic object in anti-Wick quantization, applied in the construction of time operators, and in constructing functional Hilbert spaces via the Wavelet transform. The wavelet transform is one of the more important applications of harmonic analysis on Lie groups and serves as one important unifying principle for coherent states.